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True or false? Chess will never be solved! why?


  • 3 months ago · Quote · #1161

    TheGreatOogieBoogie

    btickler wrote:

    Here's an update on the progress of using diamond to store data, which I mentioned much earlier in this thread, sometime last year:

    http://www.theregister.co.uk/2014/08/11/another_step_forward_for_diamondbased_quantum_computers/

    This is about the current limit of "foreseeable future".

    Diamond sounds unviably expensive however. 

  • 3 months ago · Quote · #1162

    btickler

    TheGreatOogieBoogie wrote:
    btickler wrote:

    Here's an update on the progress of using diamond to store data, which I mentioned much earlier in this thread, sometime last year:

    http://www.theregister.co.uk/2014/08/11/another_step_forward_for_diamondbased_quantum_computers/

    This is about the current limit of "foreseeable future".

    Diamond sounds unviably expensive however. 

    Not really.  Diamond prices are artificially inflated and have been ever since manufactured diamonds came into being; plus, the diamonds you are thinking of are mined diamonds with flaws in them...wholly unsuitable for this purpose :).

    This would use manufactured diamond "sheets", and all it takes is carbon and pressure.  Thus, "foreseeable future", aka hard science fiction vs. soft science fiction.

    Gold, silver, platinum...these are actually rare elements (because fusion inside stars only compacts to iron normally...heavier elements require a greater catalyst) that will remain hard to find or produce.  Diamonds, no.  Diamonds are made of cheap and abundant carbon.  Someday, diamond coffee tables will be commonplace.

  • 3 months ago · Quote · #1163

    TheGrobe

    Diamond is artificially expensive, there is a long standing cartel manufactured "supply shortage" created by withholding diamonds from the market.

    Diamond is also possible to synthesize.

  • 3 months ago · Quote · #1164

    TheGrobe

    Ahh, seconds too slow.

  • 3 months ago · Quote · #1165

    TheGrobe

    btickler wrote:
     Someday, diamond coffee tables will be commonplace.

    Ooh, ostentatious!

  • 3 months ago · Quote · #1166

    watcha

    100 fold increase in complexity with adding a new chessman only holds at the current level of tablebases. Two kings are 3612 positions + 30 chessmen would mean 3612 * 10^( 30 * 2 ) positions or 3.6 * 10^63 positions and it is proven that there are less than 10^46.

    When there are many chessmen on the board there are less squares to put a new chessman on and also this new chessman can't be anything due to legality issues. If apart from kings you already have 16 pawns and a white queen on board, you can't put an other white queen there, because this would be illegal. If apart from kings you have only a white queen on board, you can put there an other 8 white queens and it will still be legal. ( There are even more subtle combinatorial reasons, but I don't want to discuss them here. I have calculated complexity up to 10 men with a program that takes into account every possibility. )

    On the other hand if in positions with two kings you put a single chessman on board, you can do this is 62 * 10 ways ( 62 squares are free and there are 10 chessmen available: white / black: pawn, knight, bishop, rook, queen ). So to go from a 'two men tablebase' ( only kings ) to a three men tablebase you added complexity of 620 times insted of 100 times.

    ( Note: the above are raw estimates for completely random positions, pawns can be on the first and last rank, they can be illegal due to checks, symmetries are ignored, turn is ignored, etc. ).

    Complexity increases very quickly with adding a new chessman when there are only a few chessmen on board, then with more and more chessman on board this pace starts to slow down. Adding a new chessman to a 31 men tablebase only increases complexity in a marginal way. However this increase will be 100 times in the foreseeable future.

    Also computational power has to increase, but this is a lesser worry because theoretical limits to computational power are ridiculously high compared to limits of storage. A 1 kg computer operating at Bremermann's limit could perform operations on the order of the number of legal positions in less than a second.

  • 3 months ago · Quote · #1167

    watcha

    Combinatorially possible positions with legally placed kings ( according to my program's run ) :

     3 men: 2.24e+006

     4 men: 6.85e+008

     5 men: 1.37e+011

     6 men: 2.03e+013

     7 men: 2.36e+015

     8 men: 2.24e+017

     9 men: 1.80e+019

    10 men: 1.24e+021

  • 3 months ago · Quote · #1168

    watcha

    Some bullhit math ( bullhit means something that was hit by a bull ):

    How to build a perfect hash of all 7 men combinatorially possible positions?

    What makes this possible is that the problem can be divided into three independent parts.

    There are always two kings on the board, so first create a function h1 which maps all possible legal king arrangements to an index:

    h1 ( king arrangement ) -> 0 ... 3611

    For all king arrangements there are 62 squares to place 5 non king chessmen, this can be done in choose(62,5) = 6 471 002 ways. Create a function h2 which maps all possible occupied square arrangement to an index:

    h2 ( occupied squares ) -> 0 ... 6 471 001

    Given 5 occupied squares there are 10^5 ways to fill these places with chessmen ( order matters! ). It is trivial to create a hash function for this case, just use codes 0 ... 9 for the ten possible chessmen and write them down in the right order, you will get a number between 0 and 10^5-1:

    h3 ( chessmen arrangement ) -> 0 ... 99 999

    You can get the address at which the value of a position is stored:

    memory index = ( h1 * 6 471 002 + h2 ) * 100 000 + h3

    The only thing you have to actually store in memory is an integer per position ( 0 for draw, or +/- mate in N moves ).

    Since most of the positions are draw or mate in a couple of dozen moves, the true information content of those integers is not more than 5-6 bits / position. You can zip integers in 100 000 integer blocks to reach this compression, and unzip only the block which is queried.

    The outcome of all chess positions without castling rights is invariant under flipping the board over the vertical axis. This means that you can improve by a factor of two on the raw method. ( There are more symmetries for positions without pawns but in a typical 7 men position there will be at least one pawn. )

    Using this method the 7 men tablebase can be stored on cca. 6 * 10^15 bits.

    It is actually stored on 1.12 * 10^15 bits ( 140 TB = 140 * 10^12 * 8 = 1.12 * 10^15 bits ). So the creators of the tablebase must have used a more clever method than this.

  • 3 months ago · Quote · #1169

    SmyslovFan

    Watcha's the only one who can use bogus math in this thread.

  • 3 months ago · Quote · #1170

    watcha

    This may be easier to come to terms with: the human genome contains cca. 1 GB of information coded in DNA. This DNA is cca. 6.9 cubic micrometer in volume. This means that a 10 men tablebase can be stored in 1 cubic centimeter DNA:

  • 3 months ago · Quote · #1171

    Brazil_World

    i like it!!!

  • 3 months ago · Quote · #1172

    Doggy_Style

    Hey watcha, you're the only one who is saying anything different and thought provoking... don't let the b'stards grind you down.

  • 3 months ago · Quote · #1173

    Doggy_Style

    chessmstrmate wrote:
    Doggy_Style wrote:

    Hey watcha, you're the only one who is saying anything different and thought provoking... don't let the b'stards grind you down.

    You look like an Old DOG! that's been Well Ground down! 

    I have, on occasion, been well ground down.

     

    *Gurgle*

  • 3 months ago · Quote · #1174

    Doggy_Style

    chessmstrmate wrote:
    Doggy_Style wrote:
    chessmstrmate wrote:
    Doggy_Style wrote:

    Hey watcha, you're the only one who is saying anything different and thought provoking... don't let the b'stards grind you down.

    You look like an Old DOG! that's been Well Ground down! 

    I have, on occasion, been well ground down.

     

    *Gurgle*

    I am Sure! A.I.D.S is Rife where you live! 

    Yeah... I'm not doing this with you. Feel free to carry on though.

  • 3 months ago · Quote · #1175

    TheGrobe

    chessmstrmate wrote:
    I'm the One doing!

    What, exactly, is left to the reader's imagination.

  • 3 months ago · Quote · #1176

    watcha


    This is my estimate of tablebase complexity ( see #1187 ):

     6 men: 2.03e+013

     7 men: 2.36e+015

    It is known that the 6 men tablebase requires 1.2 TB of storage.

    To calculate the storage requirement from the complexity, you have to divide the 7 men complexity by the 6 men complexity and multiply this by 1.2 TB:

    If you do the calculation this formula predicts that the 7 men tablebase should take 139.5 TB of space.

    It is known that it uses 140 TB, so the complexity estimate predicts its size almost perfectly.

     


     

    Estimated storage requirement for tablebases up to 12 men:

     

     8 men : 13 Petabyte

     9 men : 1.1 Exabyte

    10 men : 74 Exabyte

    11 men : 4.4 Zettabyte

    12 men : 235 Zettabyte


    Storage on the order of Petabytes is already happening:

    http://information-technology.web.cern.ch/about/computer-centre

    The only organization that seems to be able to store a 9 men tablebase is NSA, which is believed to have the largest storage capacity in the world of 2 Exabytes:
     
     
    It is calculated that humanity has stored 295 Exabytes of information between 1986 and 2007:
     
  • 3 months ago · Quote · #1177

    Iluvsmetuna

    fantastic!! must remember!!

  • 3 months ago · Quote · #1178

    MuhammadAreez10

    Watcha! Gotcha!


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